Magnetic ground state of RBaCo2O5.5 „RÄTb, Gd… compounds

PHYSICAL REVIEW B 67, 094436 共2003兲

Magnetic ground state of RBaCo2 O5.5 „RÄTb, Gd… compounds Qinfang Zhang1,2 and Weiyi Zhang1,2 1

Jiangsu Provincial Laboratory for NanoTechnology and Department of Physics, Nanjing University, Nanjing 210093, China National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China 共Received 4 October 2002; revised manuscript received 21 November 2002; published 31 March 2003兲

2

The oxygen-deficient perovskites RBaCo2 O5.5 (R⫽Tb, Gd) unveil similar magnetic properties; the magnetization 关 M (T) 兴 demonstrates a sharp cusp near the magnetic transition temperature T C and a 1/T dependence at low temperature, while the remnant magnetic moments at zero temperature are small 关 ␮ ⬇(0.05–0.1) ␮ B 兴 the high temperature effective magnetic moments are rather large 关 ␮ e f f ⬇(4.7–4.9) ␮ B 兴 . We show in this paper that the paramagnetic behavior of R ions and ferrimagnetic ordering of high-spin Co⫹3 ions on both octahedron and pyramid sites can account for all above experimental observations. Our conclusion is based on the calculation within the unrestricted Hartree-Fock approximation and the real-space recursion method. Among the large number of spin and charge ordered states we considered, only the high-spin high-spin antiferromagnetically ordered state, the high-spin intermediate-spin antiferromagnetically ordered state, and the low-spin intermediate-spin ferromagnetically ordered state may become the ground state of the system as Dq increases. However, only the high-spin high-spin antiferromagnetically ordered state is consistent with the experimental findings. DOI: 10.1103/PhysRevB.67.094436

PACS number共s兲: 75.25.⫹z, 75.47.Gk

I. INTRODUCTION

One of the interesting properties of cobalt based perovskites is the spin-state transition related to the Co⫹3 moment.1– 4 It stems from the fact that the crystal-field splitting 10Dq and Hund’s coupling constant J H involve a simi4 2 e g ), a lowlar energy. Thus a high-spin state 共HS, Co⫹3 -t 2g ⫹3 6 0 spin state 共LS, Co -t 2g e g ), and an intermediate-spin state 5 1 共IS, Co⫹3 -t 2g e g ) can all occur depending on the detailed crystal structure, valence state of Co ions, as well as temperature. A much studied example is the cubic perovskite LaCoO3 . While the low temperature magnetic property clearly points to the nonmagnetic low-spin state,5 the spin state above the magnetic transition (T C ⬇90 K) is still unsettled. The high-spin state,6 intermediate-spin state,7 and high-spin low-spin nearest neighbor ordered state3,5,8 were proposed to explain the temperature dependence of magnetic susceptibility above 90 K. The discovery of giant magnetoresistance共GMR兲 in Mn based perovskites gives a further impetus to the study on Co based compounds, because a similar GMR effect, although somewhat small in magnitude, was also found in their doped variants. Since the GMR effect is closely related to the spin-state transition in cobalt based perovskites, the elucidation of the spin state became a hot topics recently not only because of its fundamental physics, but also because of the potential application in magnetic sensors and recording. In addition to cubic perovskite structures, studies were recently expanded to other types of structure of cobalt based perovskites. Among others, the oxygen deficient rare-earthbased cobaltites, LnBaCo2 O5⫹ ␦ (0⭐ ␦ ⭐1, Ln⫽rare earth兲,9–15 received most of the attention due to their large GMR effect. This family of compounds presents rich and complex phenomena such as a metal-insulator transition, spin ordering, charge ordering, as well as orbital ordering, the GMR effect results from competition among various de0163-1829/2003/67共9兲/094436共7兲/$20.00

grees of freedoms. In contrast to the cubic perovskite structure, where all Co3⫹ ions are within octahedra surrounded by six neighboring oxygens, the valence and local configurations of Co ions depend on the oxygen content. The valence of Co ions changes from 50% of Co3⫹ and 50% of Co4⫹ for ␦ ⫽1 to 50% of Co3⫹ and 50% of Co2⫹ for ␦ ⫽0. It passes through 100% of Co3⫹ for ␦ ⫽0.5. Corresponding to the above valence state, the local configuration of Co ions also changes from 100% octahedral sites, to 100% pyramidal sites, and passes through a case with 50% octahedral sites and 50% pyramidal sites for ␦ ⫽0.5. Recently, Vogt et al.16 investigated the magnetic structures of oxygen-deficient double perovskite YBaCo2 O5 using synchrotron x-ray and neutron powder diffraction measurements. It was found that YBaCo2 O5 undergoes a paramagnetic to antiferromagnetic phase transition upon cooling below T⬃330 K. Furthermore, a Co2⫹ /Co3⫹ charge and orbital ordered state appears at T CO ⫽220 K. Both Co2⫹ and Co3⫹ ions form one-dimensional chains of a stripe type along the a axis. The effective magnetic moment of Co2⫹ and Co3⫹ ions are 2.7␮ B and 4.2␮ B , respectively.16 They ascribed the magnetic moments to the HS state of Co2⫹ and the IS state of Co3⫹ . Suard et al.17 independently observed the same charge ordering in isostructural HoBaCo2 O5 , but without an anomalous spin-state transition. From measured magnetic moments of Co2⫹ (2.7␮ B ) and Co3⫹ (3.7␮ B ) ions, they concluded that both Co ions are in HS states. Similar to the experimental situation, there is also much debate as to the theoretical explanation of the spin states of Co2⫹ and Co3⫹ ions. Although both use the same local spin density approximation 共LSDA⫹U兲 method, Wu18 found that Co2⫹ and Co3⫹ ions are both in the HS state at low temperature, whereas another group19 obtained HS and IS states for Co2⫹ and Co3⫹ ions, respectively. An independent study by Wang et al.20 confirmed the conclusion reached by Wu. More recently, oxygen deficient perovskites RBaCo2 O5.5

67 094436-1

©2003 The American Physical Society

PHYSICAL REVIEW B 67, 094436 共2003兲

QINFANG ZHANG AND WEIYI ZHANG

(R⫽Tb, Gd) were also investigated by several groups.9–11 X-ray diffractions showed that the structure is characterized by a periodic arrangement of planes of octahedral CoO6 and pyramidal CoO5 along the b axis. The neutron diffraction measurement suggested that the long range magnetic ordering is a G-type antiferromagnetic state at low temperature. The transport and magnetic properties demonstrate a similar pattern; both compounds undergo a metal-insulator transition at T M I ranging from 340 to 365 K. The susceptibility is composed of two parts; a divergent tail at the low temperature range is contributed by the paramagnetic R ions which obeys the Curie law; the pronounced cusp near T C ⬇270 K is another common feature, and the mechanism of the cusp is still a controversial issue. Although the effective magnetic moment at high temperature ranges from 4.7␮ B to 4.9␮ B , and clearly indicates a high-spin state above T C , the low temperature remnant magnetic moment is quite small, and is around 0.06␮ B if the paramagnetic contribution is subtracted. The size of the magnetic moment below T C is usually inferred from the upper edge of the cusp, which resembles a ferromagnetic transition; it is also suggested that the intermediate-spin state is involved. Thus a series of magnetic transitions are invoked to explain the cusp which consists of a paramagnetic to a ferromagnetic transition at T C , a ferromagnetic to an antiferromagnetic transition at T N etc. In view of the large effective magnetic moment at high temperature and the small remnant magnetic moment in the low temperature range, it is natural to relate the cusp feature in the susceptibility curve to the property of a ferrimagnetic state formed with two antiparallel moments of different magnitudes. Unlike the oxygen deficient YBaCo2 O5 perovskites, where all Co ions have the same local environment, the RBaCo2 O5.5 (R⫽Tb, Gd) structure has two different Co sites. The octahedral and pyramidal sites have different coordination numbers of oxygen ions; this makes the on-site energies of electrons of the two sites somewhat different, as do the magnetic moments. As is well known, in ferrimagnetic materials, neighboring antiparallel moments are not compensated for completely. This gives rise to a relatively strong net magnetization 共particularly when compared to antiferromagnets兲. The cusp in the magnetization curve is another important feature of the ferrimagnetic state, although sharp and narrow cusps have not commonly been seen. Using the local spin density approximation, Wu21 was the first to address the spin states of RBaCo2 O5.5 (R⫽Tb, Gd) at various temperatures. Inspired by the d-p exchange mechanism,22 he concentrated on the paramagnetic, highspin high-spin ferromagnetic, and chain type high-spin highspin antiferromagnetic states 共HS-HS-CAFM兲; the HS-HSCAFM state was proposed to be the possible candidate at low temperature. The experimentally observed G-type antiferromagnetic state was mentioned in his paper, but no further investigation was made and energies of various states were not compared to pin down the possible magnetic ground state; the ferrimagnetic nature was also not emphasized. In order to discern the magnetic ground state in the perovskites RBaCo2 O5.5 (R⫽Tb, Gd), in this paper we study the various magnetic states of an enlarged supercell

共4-primitive cell兲. We consider all possible magnetic states resulting from spin combinations among the HS, IS, and LS of Co3⫹ ions in both octahedral and pyramidal sites. The calculation is performed within the unrestricted Hartree-Fock approximation on a realistic perovskite lattice model, and self-consistent solutions are obtained using the iteration scheme. To compare the relative stability of various states, we have computed their energies as functions of the crystalfield splitting 10Dq since, the phase diagram depends mainly on the competition between the Hund’s coupling J H and 10Dq. For a fixed J H , it is found that the ground state of RBaCo2 O5.5 (R⫽Tb, Gd) takes, consecutively, a G-type HS-HS antiferromagnetic state 共HS-HS-GAFM, both ions are in HS states兲, a G-type HS-IS antiferromagnetic state 共HS-IS-GAFM, HS for Co3⫹ ions in octahedra and IS for Co3⫹ ions in pyramids兲, and a LS-IS ferromagnetic state 共LS-IS-FM, LS for Co3⫹ ions in octahedra and IS for Co3⫹ ions in pyramids兲 as Dq increases. The HS-HS-CAFM state found by Wu21 always seems higher in energy than the HSHS-GAFM state in the relevant parameter range. In view of measured magnetic moments at both high and low temperatures as well as the temperature dependence of magnetization M (T) of polycrystalline RBaCo2 O5.5 (R⫽Tb, Gd), we conclude that the G-type HS-HS antiferromagnetic state is the most probable candidate. As is well known, the Hartree-Fock method gives, in a first-order approximation, qualitatively correct results. Better methods, such as the slave boson method, may change the results quantitatively but not qualitatively. The rest of the paper is organized in the following way. In Sec. II, we introduce the multiband d-p lattice model and the unrestricted Hartree-Fock approximation; the real-space recursion method is also briefly outlined. In Sec. III, we present the numerical results for the density of states of each state. The electron occupation numbers and magnetic moments of the spin state are computed and compared with experimental values. The energies of various spin states are calculated to determine the ground state of the compound. The conclusion is drawn in Sec. IV. II. THEORETICAL MODEL AND FORMULATION

It is now well known that the insulating state of undoped perovskite compounds is of charge transfer type.22 The doping introduces charge carriers not only to transition metal orbitals, but also to oxygen orbitals. Since the rare earth elements form paramagnetic ions which contribute little to the density of states at the Fermi energy,21 only transition metal 3d orbitals and oxygen 2p orbitals play important roles. Thus we adopt the general multiband d-p model Hamiltonian23 which takes the full degeneracies of the transition metal 3d orbitals and oxygen 2p orbitals as well as on-site Coulomb and exchange interaction into account, H⫽

094436-2

0 mn † † † d im 兺 ␧ dm ␴ d im ␴ ⫹ 兺 ␧ p p jn ␴ p jn ␴ ⫹ 兺 共 t i j d im ␴ p jn ␴ jn ␴ i jmn ␴

im ␴

⫹H.c.兲 ⫹ ⫹

兺

i jnn ⬘ ␴

⬘ † 共 t nn i j p in ␴ p jn ⬘ ␴ ⫹H.c 兲

† † ud im↑ d im↑ d im↓ d im↓ 兺 im

PHYSICAL REVIEW B 67, 094436 共2003兲

MAGNETIC GROUND STATE OF RBaCo2 O5.5 (R⫽Tb, . . .

1 † ⫹ ˜u d† d d d 2 im⫽m ⬘ ␴␴ ⬘ im ␴ im ␴ im ⬘ ␴ ⬘ im ⬘ ␴ ⬘

兺

⫺J H

兺

im ␴␴ ⬘

† ជ ជd d im ␴ ␴ d im ␴ ⬘ •S im ,

共1兲

† † where d im ␴ (d im ␴ ) and p jn ␴ (p jn ␴ ) denote the annihilation 共creation兲 operators of an electron on Co-d at site i and O-p 0 and ␧ p are their corresponding at site j, respectively, and ␧ dm on-site energies. m and n represent the orbital index, and ␴ denotes the spin. The crystal-field-splitting energy is in0 , i.e., ␧ 0d (t 2g )⫽␧ 0d ⫺4Dq 共octahedra兲, ␧ 0d (e g ) cluded in ␧ dm 0 ⫽␧ d ⫹6Dq 共octahedra兲, ␧ 0d (d x 2 ⫺y 2 )⫽␧ 0d ⫹9.144Dq 共pyramids兲, ␧ 0d (d 3z 2 ⫺r 2 )⫽␧ 0d ⫹0.86Dq 共pyramids兲, ␧ 0d (d xy )⫽␧ 0d ⫺0.86Dq 共pyramids兲, and ␧ 0d (d yz )⫽␧ 0d (d xz )⫽␧ 0d ⫺4.57Dq 共pyramids兲, where ␧ 0d is the bare on-site energy of the d nn ⬘ orbital. t mn are the nearest neighbor hopping intei j and t i j grals for p-d and p-p, which are expressed in terms of Slater-Koster parameters (pd ␴ ), ( pd ␲ ), ( pp ␴ ), and d is the total spin operator of the Co ion extracting ( p p ␲ ). Sជ im the spin operator in orbital m. The parameter J H is the Hund’s coupling constant, ˜u ⫽u⫺5J H /2, and u is related to the multiplet averaged d-d Coulomb interaction U via u ⫽U⫹(20/9)J H . In the unrestricted Hartree-Fock approximation, Eq. 共1兲 may be reduced to the following single particle Hamiltonian:

H⫽

兺 im ␴

冋

d

0 ␧ dm ⫹un im ¯␴ ⫺

JH ␴ 共 ␮ dt ⫺ ␮ md 兲 2

册

d † ˜ 共 n dt ⫺n m ⫹u 兲 d im ␴ d im ␴ ⫹

⫹ ⫹

␧ p p †jn ␴ p jn ␴ 兺 jn ␴

兺

† 共 t mn i j d im ␴ p jn ␴ ⫹H.c 兲

兺

⬘ † 共 t nn i j p in ␴ p jn ⬘ ␴ ⫹H.c. 兲 .

i jmn ␴

i jnn ⬘ ␴

共2兲

d d d d d d † Here n m ␴ ⫽ 具 d m ␴ d m ␴ 典 , ␮ m ⫽n m↑ ⫺n m↓ , and n t and ␮ t are the total electron number and magnetization of the Co-d orbitals. We have chosen the z axis as the spin quantization axis. For the tight-binding Hamiltonian 关Eq. 共2兲兴, the density of states can be easily calculated using the real-space recursion method24 and the Green’s function is expressed as

b 20

0 Gm ␴共 ␻ 兲 ⫽

b 21

␻ ⫺a 0 ⫺

b 22

␻ ⫺a 1 ⫺ ␻ ⫺a 2 ⫺

b 23

␻ ⫺a 3 ⫺•••.

共3兲

The recursion coefficients a i and b i are obtained from the tridiagonalization of the tight-binding Hamiltonian matrix

for a given starting orbital. The multiband terminator25 is chosen to close the continuous fractional. In order to investigate all possible ground states of RBaCo2 O5.5 (R ⫽Tb, Gd), we have considered various ordered states of an enlarged quadruple cell of RBaCo2 O5.5 (R⫽Tb, Gd), and computed 31 levels for each of the 106 independent orbitals. Our results have been checked for different levels to secure the energy accuracy better than 5 meV. The whole procedure is iterated self-consistently until convergence and the density of states are obtained by ␳ m ␴ ( ␻ )⫽⫺(1/ ␲ )Im G m ␴ ( ␻ ), which allows us to compute the electron numbers and magnetic moments as well as the energies of various ordered states. III. NUMERICAL RESULTS AND DISCUSSIONS

Although the direct parameters of RBaCo2 O5.5 (R ⫽Tb, Gd) are not available, their values can be inferred from those of LaCoO3 . 5,8 The bare on-site energies of the O-p orbital is taken as the energy reference point ␧ p ⫽0 eV. Those of Co-d orbitals of octahedra and pyramids depend on 0 the crystal field of neighboring oxygen ions, ␧ d,octa. 0 ⫽⫺26 eV and ␧ d,pyra. ⫽⫺28 eV. The on-site Coulomb repulsion and Hund’s coupling constant are set as U⫽5.0 eV and J H ⫽0.84 eV. 3 The Slater-Koster parameters are estimated from those of LaCoO3 using well known scaling relations:26 V ll ⬘ m ⬀d ⫺2 for l⫽l ⬘ ⫽1 and V ll ⬘ m ⬀d ⫺3.5 for l⫽1, l ⬘ ⫽2, where d is the distance between two atoms. To describe the Slater-Koster parameters between the different pairs of atoms, we denote the cobalt atoms in octahedral and 1 2 pyramidal sites by Co共1兲 and Co共2兲; O ab (O ab ) and O 1c (O 2c ) stand for oxygens in the ab plane and along the c axis in the octahedrons 共pyramids兲, respectively. Using the bond lengths listed in Ref. 15, the Slater-Koster parameters within the octahedrons and the pyramids are listed in Table I. With the parameter set given above, we have studied the electronic structures of various spin-states as functions of the crystal-field splitting Dq. Eight magnetic structures with different spin-state combinations are found to be metastable. They are the G-type HS-HS antiferromagnetically ordered state 共HS-HS-GAFM, where the first HS refers to the highspin state of Co⫹3 ions in octahedral sites, the second HS refers to the high-spin state in pyramidal sites; nearest Co⫹3 moments are ordered antiferromagnetically兲, the G-type HS-IS antiferromagnetically ordered state 共HS-IS-GAFM兲, the G-type IS-IS antiferromagnetically ordered state 共IS-ISGAFM兲, the C-type HS-HS antiferromagnetically ordered state 共HS-HS-CAFM, Co⫹3 moments are ordered ferromagnetically along a-axis, and antiferromagnetically ordered along b and c-axis, respectively兲, the C-type HS-IS antiferromagnetically ordered state 共HS-IS-CAFM兲, the IS-IS ferromagnetically ordered state 共IS-IS-FM兲, the LS-IS ferromagnetically ordered state 共LS-IS-FM兲, and the LS-LS paramagnetic state 共LS-LS-PM兲. In order to compare the relative stability of all eight states, their energies as functions of Dq are presented in Fig. 1. In the parameter range 0.10 ⭐Dq⭐0.20, three magnetic structures may become a ground state of the system. They are the HS-HS-GAFM state for Dq⬍0.14 eV, HS-IS-GAFM state for 0.14⬍Dq

094436-3

PHYSICAL REVIEW B 67, 094436 共2003兲

QINFANG ZHANG AND WEIYI ZHANG

TABLE I. The Slater-Koster parameters used for RBaCo2 O5.5 (R⫽Tb, Gd) compounds, the values within the brackets are those referred to LaCoO3 compounds. 1 and 2 stand for octahedral and pyramidal sites, and a, b, and c represent the crystal axes. Bond type Co(1)⫺O 1ab Co(1)⫺O 1c O 1ab ⫺O 1ab O 1c ⫺O 1ab Co(2)⫺O 2ab Co(2)⫺O 2c O 2ab ⫺O 2ab O 2c ⫺O 2ab

pd ␴

pd ␲

0.956⫻(⫺2.0 eV) 1.140⫻(⫺2.0 eV)

0.956⫻(0.922 eV) 1.140⫻(0.922 eV)

0.988⫻(⫺2.0 eV) 1.050⫻(⫺2.0 eV)

pp ␴

pp ␲

0.986⫻(0.6 eV) 1.045⫻(0.6 eV)

0.986⫻(⫺0.15 eV) 1.045⫻(⫺0.15 eV)

1.026⫻(0.6 eV) 0.851⫻(0.6 eV)

1.026⫻(⫺0.15 eV) 0.851⫻(⫺0.15 eV)

0.988⫻(0.922 eV) 1.050⫻(0.922 eV)

⬍0.185 eV, and LS-IS-FM state for Dq⬎0.185 eV, respectively. Other states we studied are energetically unfavorable in comparison with these three states. In the following, we are mainly interested in the three possible magnetic ground states, and other states will be discussed only briefly. We first consider the HS-HS-GAFM state. This state is of interest because it has the right magnitudes of the effective paramagnetic moment above T C , and a small remnant magnetic moment at low temperature. For Dq⫽0.12 eV, the total density of states 共TDOS兲 and partial densities of states 共PDOS兲 are presented in Fig. 2. As can be seen from the TDOS 关Fig. 2共a兲兴, this state is an insulator since the Fermi energy (E F ⬅0) lies within the energy gap. The analysis of the PDOS 关Figs. 2共b兲–2共d兲兴 reveals that the DOS below E F is mainly contributed by O-p orbitals, and the peaks above the Fermi energy come mainly from the down-spin of the Co共1兲-d orbitals and the upper spin of the Co共2兲-d orbitals. The peaks near the bottom and top of the valence band stem from t 2g orbitals of Co共1兲 and Co共2兲 ions. The occupancies ⫽6.43 and n Co(2) ⫽6.59; the values of the d bands are n Co(1) d d are larger than six electrons due to the charge transfer from O-p to Co-d orbitals. The corresponding magnetic ⫽3.50␮ B ( ␮ e f f ⫽4.3␮ B ) and ␮ Co(2) moments are ␮ Co(1) d d ⫽⫺3.39␮ B ( ␮ e f f ⫽4.15␮ B ). The net moment per Co is

FIG. 1. The energies per double cell of the various spin states as a function of Dq. Other parameters are described in the text.

0.06␮ B . Since the HS-HS-GAFM state is the ground state of the compound when the crystal-field-splitting Dq ⬍0.14 eV, this range includes the commonly adopted value Dq⫽0.12 eV used in YBaCo2 O5 compound.20 Also, the ferrimagnetic nature of this state suggests that cusp feature can occur in susceptibility curve though the detailed form needs further investigation. Thus, we conclude that this state is the most probable candidate for the ground state of RBaCo2 O5.5 (R⫽Tb, Gd). Another interesting spin state is the HS-IS-GAFM state, obtained when an electron is demoted from d x 2 ⫺y 2 orbital to d yz orbital of Co3⫹ (2) ions. The densities of states are calculated for Dq⫽0.16 eV, and plotted in Fig. 3; it is found

FIG. 2. The spin resolved densities of states of the HS-HSGAFM state. 共a兲 TDOS, 共b兲 PDOS of Co共1兲-d, and 共c兲 PDOS of Co共2兲-d, 共d兲 PDOS of O-p. Dq⫽0.12 eV, and other parameters are described in the text.

094436-4

PHYSICAL REVIEW B 67, 094436 共2003兲

MAGNETIC GROUND STATE OF RBaCo2 O5.5 (R⫽Tb, . . .

FIG. 3. The spin resolved densities of states of the HS-ISGAFM state. 共a兲 TDOS, 共b兲 PDOS of Co共1兲-d, 共c兲 PDOS of Co共2兲d, and 共d兲 PDOS of O-p. Dq⫽0.16 eV, and other parameters are described in the text.

that the overall shape of the densities of states are quite similar to those of HS-HS-GAFM state. However, the total bandwidth resulting from Co3⫹ (2)-d orbitals are somewhat narrower than that of the HS-HS-GAFM state, since the IS state has a smaller magnetic moment and thus corresponds to a smaller exchange field. Like the HS-HS-GAFM state, the HS-IS-GAFM state is also an insulator. The electron occu⫽6.41 and n Co(2) ⫽6.75, and the correpancies are n Co(1) d d sponding magnetic moments are ␮ Co(1) ⫽3.52␮ B and d ␮ Co(2) ⫽⫺1.78 ␮ . Although this spin state can also be staB d bilized and become a ground state when 0.14⬍Dq ⬍0.185 eV, and its antiferromagnetic properties have some resemblance to the low temperature state, the remnant magnetic moment is too large in comparison with the experimentally measured value. The third spin state we considered is the LS-IS-FM state, which was originally proposed by Maignan et al.10 to describe the spin state just below the magnetic transition. Its TDOS and spin resolved PDOS, shown in Fig. 4, are calculated for Dq⫽0.2 eV. There is a small, but finite, density of states at the Fermi energy (E F ⬅0), and the LS-IS state corresponds to a bad metal. The peaks below and just above the Fermi energy come mostly from the occupied t 2g orbitals of Co共1兲 and the unoccupied t 2g orbitals of Co共2兲; the broad feature below the Fermi energy is mainly contributed by the O-p orbitals. The e g orbitals of Co共1兲 are located above the Fermi energy and are nearly unoccupied. The electron occu⫽6.65 and n Co(2) ⫽6.68, and the correpancies are n Co(1) d d

FIG. 4. The spin resolved densities of states of the LS-IS-FM state. 共a兲 TDOS, 共b兲 PDOS of Co共1兲-d, 共c兲 PDOS of Co共2兲-d, and 共d兲 PDOS of O-p. Dq⫽0.20 eV, and other parameters are described in the text.

sponding magnetic moments are ␮ Co(1) ⫽0.016␮ B and d ␮ Co(2) ⫽1.968 ␮ , respectively. In view of the large remnant B d magnetic moment and ferromagnetic ordering, this state is also not qualified for the ground state of the compound. Besides the three spin states discussed above, there are five other metastable states of spin combinations. Since these states are not global minima in any of the parameter ranges, we shall only describe them briefly in the following. In Fig. 5, the total densities of all five spin states are illustrated, the crystal-field-splitting Dq⫽0.12 eV. The solid and dotted lines denote the upper-spin and down-spin density of states, respectively. The first state presented in Fig. 5共a兲 is the LSLS-PM state. The absence of an exchange field eliminates the exchange splitting of the bands, the total bandwidth looks narrow, and the system is also a bad metal. The electron ⫽6.65 and n Co(2) ⫽6.83. This state is occupancies are n Co(1) d d recognized as the ground state of cubic perovskite LaCoO3 , where the compound is an insulator due to a larger Dq ⫽0.16 eV. However, this state is not energetically favorable for the oxygen deficient perovskite structures, as indicated in Fig. 1. The second state is the IS-IS-FM state plotted in Fig. 5共b兲, and is a half metal with a relatively high density of states at the Fermi energy. The electron occupancies are ⫽6.53 and n Co(2) ⫽6.88, and the magnetic moments n Co(1) d d Co(1) are ␮ d ⫽1.86␮ B and ␮ Co(2) ⫽2.32␮ B . The third state is d the HS-HS-CAFM state; this state was fully investigated by Wu21 and chosen as a candidate for the postulated spin state at low temperature. Unfortunately, the HS-HS-CAFM state is always much higher in energy than the HS-HS-GAFM state 共Fig. 1兲. Similar to the HS-HS-GAFM state, the HS-HS-

094436-5

PHYSICAL REVIEW B 67, 094436 共2003兲

QINFANG ZHANG AND WEIYI ZHANG

didate for the magnetic state at low temperature. The HS-HSGAFM state was also mentioned in his paper concerning bandwidth, but no band structures were given and relative stability was not analyzed in comparison with other spin states. In fact, the magnetic ground state HS-HS-GAFM we find is quite similar to the spin-state HS-HS-CAFM found by Wu; both involve high-spin Co⫹3 ions and antiferromagnetic ordering plays a significant role in both states. The difference between the two states lies in the ferromagnetic component along a axis which is present in the HS-HS-CAFM state, but absent in the HS-HS-GAFM state. According to Anderson’s theory, superexchange interaction usually occurs for insulating system without level degeneracy. This is the case in the oxygen deficient perovskite RBaCo2 O5.5 (R⫽Tb, Gd), where the crystal field splitting removes the degeneracy among d x 2 ⫺y 2 and d 3z 2 ⫺r 2 orbitals. The situation is quite different for the LaMnO3 compound; the degeneracy of e g orbitals makes Mn3⫹ ions Jahn-Teller, active which results in an antiferro-orbital ordering and a corresponding ferromagnetic long range order in the ab plane. The reason that highspin states become ground states at low Dq is because of the competition between crystal field splitting and Hund’s coupling; low Dq makes the Hund’s coupling dominant. FIG. 5. The spin resolved total densities of states for 共a兲 LS-LSPM, 共b兲 IS-IS-FM, 共c兲 HS-HS-CAFM, 共d兲 HS-IS-CAFM, and 共e兲 IS-IS-GAFM states. Dq⫽0.12 eV, and other parameters are described in the text.

CAFM state is also an insulator and its total DOS is shown in Fig. 5共c兲. The gross feature is very close to that of the HS-HS-GAFM state except for the narrower bandwidth. The ⫽6.41 and n Co(2) ⫽6.53, and electron occupancies are n Co(1) d d the magnetic moments are ␮ Co(1) ⫽3.53 ␮ and ␮ Co(2) B d d ⫽⫺3.43␮ B . Another convergent antiferromagnetic state is the HS-IS-CAFM state plotted in Fig. 5共d兲, which also corresponds to a metallic state. The electron occupancies are ⫽6.38 and n Co(2) ⫽6.79; their magnetic moments are n Co(1) d d Co(1) ␮d ⫽3.50␮ B and ␮ Co(2) ⫽⫺1.95␮ B . The last convergent d state is the IS-IS-GAFM state. Judging from the density of states shown in Fig. 5共e兲, it is a metal. The electron occupan⫽6.57 and n Co(2) ⫽6.75, and the magnetic cies are n Co(1) d d moments are ␮ Co(1) ⫽1.86␮ B and ␮ Co(2) ⫽⫺1.77␮ B . d d As we described in Sec. I, Wu21 was the first to address the spin state in the oxygen deficient perovskite RBaCo2 O5.5 (R⫽Tb, Gd). Motivated by the d-p exchange concept,22 he suggested that the HS-HS-CAFM state is the probable can-

1

W. C. Koehler and E. O. Wollan, J. Phys. Chem. Solids 2, 100 共1957兲. 2 J. B. Goodenough, J. Phys. Chem. Solids 6, 287 共1958兲. 3 Min Zhuang, Weiyi Zhang, and Naiben Ming, Phys. Rev. B 57, 10 705 共1998兲. 4 S. Yamaguchi, Y. Okimoto, and Y. Tokura, Phys. Rev. B 55, R8666 共1997兲.

IV. CONCLUSION

In this paper, we have investigated the various spin states of an enlarged supercell 共4-primitive cell兲 of RBaCo2 O5.5 (R⫽Tb, Gd) using the unrestricted Hartree-Fock approximation of the multiband d-p model. Eight different magnetic structures are found to be metastable and the energy diagrams are obtained as functions of the crystal field splitting. Based on the measured effective magnetic moments at high temperature, the remnant magnetic moment at low temperature, as well as the cusp feature of the ferrimagnetic state, we conclude from our study that the HS-HS-GAFM state is the most probable candidate for the ground state of RBaCo2 O5.5 (R⫽Tb, Gd). As the temperature increases, a magnetic transition takes place between a ferrimagnetic state 共HS-HSGAFM兲 and a paramagnetic state. ACKNOWLEDGMENTS

The present work was supported in part by the National Natural Science Foundation of China under Grant Nos. 19934003, 90103022 and the ‘‘Excellent Youth Foundation’’ 关10025419兴 as well as the ‘‘Climbing Program’’ of NSTC关G19980614兴.

5

˜ arı´s-Rodrı´guez and J. B. Goodenough, J. Solid State M. A. Sen Chem. 116, 224 共1995兲. 6 S. Yamaguchi, Y. Okimoto, H. Taniguchi, and Y. Tokura, Phys. Rev. B 53, R2926 共1996兲; M. A. Korotin, S. Yu Ezhov, I. V. Solovyev, V. I. Anisimov, D. I. Khomskii, and G. A. Sawatzky, Phys. Rev. B 54, 5309 共1996兲. 7 T. Saitoh, T. Mizokawa, A. Fujimori, M. Abbate, Y. Takeda, and

094436-6

PHYSICAL REVIEW B 67, 094436 共2003兲

MAGNETIC GROUND STATE OF RBaCo2 O5.5 (R⫽Tb, . . . M. Takano, Phys. Rev. B 55, 4257 共1997兲. P. M. Raccah and J. B. Goodenough, Phys. Rev. 155, 932 共1967兲. 9 Y. Moritomo, T. Akimoto, M. Takeo, A. Machida, E. Nishibori, M. Takata, M. Sakata, K. Ohoyama, and A. Nakamura, Phys. Rev. B 61, R13 325 共2000兲. 10 A. Maignan, C. Martin, D. Pelloquin, N. Nguyen, and B. Raveau, J. Solid State Chem. 142, 247 共1999兲. 11 ˜ oz, A. Llobet, and M. A. G. Aranda, C. Frontera, J. L. Garcia-Mun Phys. Rev. B 65, 180405 共2002兲. 12 S. Roy, M. Khan, Y. Q. Guo, J. Craig, and N. Ali, Phys. Rev. B 65, 064437 共2002兲. 13 C. Martin, A. Maignan, D. Pelloquin, N. Nguyen, and B. Raveau, Appl. Phys. Lett. 71, 1421 共1997兲. 14 D. D. Khalyavin, I. O. Troyanchuk, N. V. Kasper, Q. Huang, J. W. Lynn, and H. Szymczak, J. Mater. Res. 17, 838 共2002兲. 15 ´ . G. Aranda, ˜ oz, M. A M. Respaud, C. Frontera, J. L. Garcı´a-Mun B. Raquet, J. M. Broto, H. Rakoto, M. Goiran, A. Llobet, and J. Rodrı´guez-Carvajal, Phys. Rev. B 64, 214401 共2001兲. 8

16

T. Vogt, P. M. Woodward, P. Karen, B. A. Hunter, P. Henning, and A. R. Moodenbaugh, Phys. Rev. Lett. 84, 2969 共2000兲. 17 E. Suard, F. Fauth, V. Caignaert, I. Mirebeau, and G. Baldinozzi, Phys. Rev. B 61, 11 871 共2000兲. 18 Hua Wu, Phys. Rev. B 62, 11 953 共2000兲. 19 S. K. Kwon and B. I. Min, Phys. Rev. B 62, 14 637 共2000兲. 20 J. Wang, Weiyi Zhang, and D. Y. Xing, Phys. Rev. B 64, 064418 共2001兲. 21 Hua Wu, Phys. Rev. B 64, 092413 共2001兲. 22 G. M. Zhao, Phys. Rev. B 62, 11 639 共2000兲. 23 T. Mizokawa and A. Fujimori, Phys. Rev. B 54, 5368 共1996兲. 24 V. Heine, R. Haydock, and M. J. Kelly, in Solid State Physics: Advances in Research and Applications, edited by H. Ehrenreich, F. Seitz, and D. Turnbull 共Academic, New York, 1980兲, Vol. 35, p. 215. 25 R. Haydock and C. M. M. Nex, J. Phys. C 17, 4783 共1984兲. 26 Walter A. Harrison, in Electronic Structure and the Properties of Solids 共Freeman, San Francisco, 1980兲.

094436-7